Solve frac{x^{2}y^{3}}{x^{4}y^{2}}*10x^5y^5/5x^5y^8

$$\frac { x ^ { 2 } y ^ { 3 } } { x ^ { 4 } y ^ { 2 } } \cdot \frac { 10 x ^ { 5 } y ^ { 5 } } { 5 x ^ { 5 } y ^ { 8 } }$$

Evaluate

$$\frac{2}{\left(xy\right)^{2}}$$

Solution Steps

Cancel out x^{2}y^{2} in both numerator and denominator.

$$\frac{y}{x^{2}}\times \frac{10x^{5}y^{5}}{5x^{5}y^{8}}$$

Cancel out 5x^{5}y^{5} in both numerator and denominator.

$$\frac{y}{x^{2}}\times \frac{2}{y^{3}}$$

Multiply \frac{y}{x^{2}} times \frac{2}{y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y\times 2}{x^{2}y^{3}}$$

Cancel out y in both numerator and denominator.

$$\frac{2}{x^{2}y^{2}}$$

Differentiate w.r.t. x

$$-\frac{4}{y^{2}x^{3}}$$